Live briefing
Everything about Collocation method
Mathematical method for approximating solutions to differential and integral equations
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations. The idea is to choose a finite-dimensional space of candidate solutions and a number of points in the domain, and to select that solution which satisfies the given equation at the collocation points. Wikipedia ā
š§ Start here: a 6-step reading path
- Read the overview: Collocation methodA 5-minute orientation
- Skim a recent paper: Stabilized Lagrange Interpolation Collocation Method: A meshfree method incorporating the advantages of finite element methodInfluential work since 2022
- Pick up a classic book: Single-grid spectral collocation for the Navier-Stokes equationsThe most-reprinted book on the subject
- Read the landmark paper: A collocation method for boundary value problemsCited 272 times
- Go sideways: GaussāLegendre methodA closely related topic
- Go sideways: RungeāKutta methodsA closely related topic
š Definitions
No dictionary entry for this exact phrase.
šļø The subject at a glance
š Landmark papers (most cited)
A collocation method for boundary value problems
Fractional Spectral Collocation Method
Leastāsquares collocation meshless method
An isogeometric collocation method using superconvergent points
The variational collocation method
Superconvergent gradient smoothing meshfree collocation method
Sinc-Collocation method for solving astrophysics equations
Collocation method for fractional quantum mechanics
š Influential since 2022
Stabilized Lagrange Interpolation Collocation Method: A meshfree method incorporating the advantages of finite element method
Barycentric rational collocation method for fractional reaction-diffusion equation
A meshfree point collocation method for elliptic interface problems
Linear barycentric rational collocation method for solving biharmonic equation
Chebyshev collocation method for fractional Newell-Whitehead-Segel equation
š Books worth reading
- šSingle-grid spectral collocation for the Navier-Stokes equationsChristine Bernardi Ā· 1988
Trefftz And Collocation MethodsH. Cheng Ā· 2008
Splines and variational methodsP. M. Prenter Ā· 1975- šA two dimensional Chebyshev collocated multi-domain algorithm for the incompressible Navier-Stokes equationsA. Pinelli Ā· 1993
- šFourier analysis of finite element preconditioned collocation schemesM. O. Deville Ā· 1990
- šSpurious modes in spectral collocation methods with two non-periodic directionsS. Balachandar Ā· 1992
- šSpectral collocation methodsM. Yousuff Hussaini Ā· 1987
- šFourier analysis of finite element preconditioned collocation schemesMichel O. Deville Ā· 1990
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
š Related topics
- GaussāLegendre method In numerical analysis and scientific computing, the GaussāLegendre methods are a family of numerical methods for ordinary differential equations. GaussāLegendreā¦
- RungeāKutta methods In numerical analysis, the RungeāKutta methods (English: /ĖrŹÅÉĖkŹtÉĖ/ RUUNG-É-KUUT-tah) are a family of explicit and implicit iterative methods, whichā¦
- Trapezoidal rule (differential equations) In numerical analysis and scientific computing, the trapezoidal rule is a numerical method to solve ordinary differential equations derived from the trapezoidalā¦
- Numerical methods for ordinary differential equations Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equationsā¦
- RungeāKuttaāFehlberg method In mathematics, the RungeāKuttaāFehlberg method (or Fehlberg method) is an algorithm in numerical analysis for the numerical solution of ordinary differentialā¦
- Spectral element method In the numerical solution of partial differential equations, a topic in mathematics, the spectral element method (SEM) is a formulation of the finite elementā¦
- List of RungeāKutta methods RungeāKutta methods are methods for the numerical solution of the ordinary differential equation d y d t = f ( t , y ) . {\displaystyle {\frac {dy}{dt}}=f(tā¦
- RungeāKutta method (SDE) In mathematics of stochastic systems, the RungeāKutta method is a technique for the approximate numerical solution of a stochastic differential equationā¦